Average Error: 0.3 → 0.2
Time: 16.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
double f(double x, double y, double z) {
        double r930159 = x;
        double r930160 = y;
        double r930161 = r930160 - r930159;
        double r930162 = 6.0;
        double r930163 = r930161 * r930162;
        double r930164 = z;
        double r930165 = r930163 * r930164;
        double r930166 = r930159 + r930165;
        return r930166;
}
↓
double f(double x, double y, double z) {
        double r930167 = y;
        double r930168 = x;
        double r930169 = r930167 - r930168;
        double r930170 = 6.0;
        double r930171 = z;
        double r930172 = r930170 * r930171;
        double r930173 = fma(r930169, r930172, r930168);
        return r930173;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)}\]

  3. Final simplification0.2

    \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot z, x\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))